In an atom 2K, 8L, 8M, 2N electrons are present If m = O, s = 1/2 then find no. of `e^(Θ)` :-

Options

A. 6
B. 2
C. 8
D. 16

Explanation

To solve the question, we need to determine the number of electrons with the specified quantum numbers in the given atom configuration. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the Total Number of Electrons
We are given the distribution of electrons in different shells:
- K shell: 2 electrons
- L shell: 8 electrons
- M shell: 8 electrons
- N shell: 2 electrons

**Total electrons = 2 (K) + 8 (L) + 8 (M) + 2 (N) = 20 electrons**

### Step 2: Write the Electron Configuration
The electron configuration for the total of 20 electrons can be written as follows:
- 1s² (2 electrons)
- 2s² (2 electrons)
- 2p⁶ (6 electrons)
- 3s² (2 electrons)
- 3p⁶ (6 electrons)
- 4s² (2 electrons)

So, the complete electron configuration is:
**1s² 2s² 2p⁶ 3s² 3p⁶ 4s²**

### Step 3: Identify the Quantum Numbers
We are given:
- m (magnetic quantum number) = 0
- s (spin quantum number) = 1/2

The magnetic quantum number (m) indicates the orientation of the orbital. For s orbitals, m can only be 0.

### Step 4: Determine the Electrons with Given Quantum Numbers
Since m = 0 corresponds to the s orbitals, we need to find the electrons in the s orbitals:
- 1s² contributes 2 electrons (m = 0)
- 2s² contributes 2 electrons (m = 0)
- 3s² contributes 2 electrons (m = 0)
- 4s² contributes 2 electrons (m = 0)

Thus, the total number of electrons in the s orbitals is:
**2 (from 1s) + 2 (from 2s) + 2 (from 3s) + 2 (from 4s) = 8 electrons**

### Step 5: Consider the Spin Quantum Number
The spin quantum number s can be +1/2 or -1/2. Each s orbital can hold a maximum of 2 electrons, one with spin +1/2 and one with spin -1/2. Since we have 8 electrons in the s orbitals, we can have:
- 4 electrons with spin +1/2
- 4 electrons with spin -1/2

### Final Answer
The total number of electrons with the specified quantum numbers (m = 0, s = +1/2) is **4**.

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